An energy landscape-based theoretical framework for understanding the self-organization of functions in a living system under the dynamical component interaction

In a living system composed of interacting components such as molecules, cells, and tissues, each component often changes its internal states in response to interactions with its surrounding components. For example, individual tissues exhibit component-level responsive behavior, such as growth and remodeling, in response to their mechanical interactions, resulting in the self-organization of functions of a multi-tissue system. Along with the responsive behavior of the components, their interactions exhibit dynamical changes, which strongly influence the self-organization of system functions. To understand how the self-organization of system functions occurs from such dynamical interactions due to component-level responsive behavior, this study proposes a theoretical framework that formulates the dynamics of interactions among components due to the component-level responsive behavior. For modeling the responsive internal state changes, we assign an energy landscape and its associated energy rate landscape for each component, leading to the generalized gradient flow model of responsive behavior. Then, we represent interaction dynamics based on temporal changes in these energy and energy rate landscapes by formulating temporal changes in the environmental states of each component due to the responsive behavior of individual components. Through case studies using simplified models of mechanically interacting tissues under morphological changes, our theoretical framework demonstrates that temporal changes in applied forces due to morphological changes of individual tissues determine the self-organization of system functions. These findings highlight that expressing interaction dynamics based on temporal changes in energy and energy rate landscapes offers a powerful theoretical framework for understanding how component-level responsive behavior organizes system functions.